Plural formations in several Afro-Asiatic languages are notoriously complex, especially Cushitic, but also Semitic languages that retain 'broken plurals'. Berber is no exception to this trend, but as it stands, no thorough description of Berber plural formations have been made from a historical perspetive. This post will try to give a bit of an overview of some of the forms found, and the problems we find.
First there is the 'sound' plural in Berber. This is marked by a prefix *a- in the singular and *i- with a suffix *-ăn in the plural of the masculine, and a prefix *ta- with a suffix *-t in the singular and *t- with a suffix *-en of the feminine. 
a-maziġ pl. imaziġ-ăn
ta-maziġ-t pl. t-mazig-en
Some variations on the plural suffix exist, of which m. *-awăn f. *-awen is certainly the most common.
The second form is the "regular" broken plural formation, which inserts a long vowel a before the last consonant and shifts a preceding vowel ă, a to ŭ, u. This formation was discussed in more detail in an earlier blogpost.
But besides this apophonic plural, there are other types of apophonic plural, these plurals generally have some form of plural suffix, but also undergo internal changes. The first group has an effect on a small but salient group of nouns in Berber. These nouns change their root vowel to *a  and lengthen the final radical of their root. Finally, a plural suffix *-ăn is added, regardless of gender (although feminine nouns in this group are few, and perhaps limited to the one example given below).
*a-ʔfud pl. *i-ʔfadd-ăn 'knee'
*a-fuʔs pl. *i-fass-ăn 'hand' 
*a-ḍar pl. *i-ḍarr-ăn 'leg'
*ta-ġaḍ-t pl. *t-ġaṭṭ-ăn 'goat'
One notices a semantic link between several of these nouns, as many (but not all) represent body parts. This may be an old distribution, or simply the way the plural formation got reanalyzed, and was subsequently spread by analogy.
Another quite common apophonic plural which is seemingly limited to masculine nouns is those that have a plural suffix -an. This formation seems to only apply to nouns with three rootconsonants, and the root consonants are reconfigured to form the shape CəCC in the plural.
*a-ǵəllid pl. *i-ǵəld-an ‘king’
*a-ḱsum pl. i-ḱəsm-an ‘meat’
*a-mǵər pl. *i-məǵr-an ‘sickle’
*a-lǔġəm pl. *i-lĭġm-an ‘camel’
As you can see, the original shape of the singular seems to be irrelavant for the plural formation. Moreover, it is perhaps possible to consider the a of the plural prefix an as a sort of suffix < *ah-ăn, compare, perhaps Ar. rafīq pl. rufaqāʔ 'companion'.
The lack of labialisation in MA alġəm/alġʷəm pl. ileġman 'camel' seems to suggest that the root vowel of the plural formation has a *ĭ, rather than *ŭ.
An interesting, final form of apophonic plurals seem like the are interesting break with the sg. *a- pl. *i- system. It concerns nouns that have an initial vowel *i in the singular that is part of the root, rather than part of the prefix. This prefix *i is changed to *a and apparently depending on the amount of consonants the word has, a suffix -ăn or -awăn (sometimes -iwăn) is added. Many languages lose this plural formation altogether, but one often finds it in the same words in very diverse languages, which let us safely reconstruct it for Proto-Berber
*iləs pl. *alsawăn 'tongue', cf. MA iləs pl. alsiwən; Fig. iləs pl. alsawən; Zng. ətʸši pl. ätʸšūn
*iġăf pl. *aġfawăn 'head', cf. Kb. ixəf pl. axfawən; Zng. iʔf pl. äʔfūn/oʔfūn
*isk pl. *askawăn 'horn', cf. MA išš pl. aššiwn; Zng. təskäh pl. täskūn, several languages appear to have formed a new singular *askaw on basis of the plural, to 'avoid' this unusual singular-plural formation, e.g. Ghd. aškaw pl. aškáwăn
*iskăr pl. *askarăn 'nail', cf. MA iššər pl. aššarn; Fig. iššər pl. aššarən; To. eskăr pl. askarăn; Note that this noun does not only change its initial vowel, but also the vowel before the last root consonant. This seems to be a way to emulate the |aCCaCăC| pattern found in the biconsonantal nouns of this type.
Once again, we are dealing with a morphological pattern that clearly does not treat long vowels as simply the result of short vowel + *h as a similar plural pattern is not attested for roots with three consonants.
 The feminine plural prefix is more traditionally reconstructed with a prefix *ti-. I've recently presented a paper on this at NACAL. The slides and handout can be found on my Academia page. Hopefully this paper will be published in a more fleshed out form soon.
 But in Ghadames and Nefusi, a short vowel *ă replaces the root vowel rather than *a
 The loss of the glottal stop in this plural is not well-understood, but seems to be real: Zng. ävuʔš pl. uvässän / uṿässän. While it is difficult to evaluate, Ghadames seems to confirm the absence of the glottal stop ófəss pl. făssăn. Pre-Ghd. *i-făʔssăn should have yielded *fossăn. Was there a constraint against CCC clusters in Proto-Berber which simplied *ʔss > *ss?